In this paper, we propose efficient numerical techniques for Butterworth filtering and implicit fairing of large irregular triangle meshes, where the corresponding filters are rational polynomials and the resulting large linear systems need to be solved iteratively. We show that significant speed-up can be achieved for Butterworth filtering by factorizing the linear system in the complex domain...

We present and study a homographic best approximation problem, which arises in the analysis of waveform relaxation algorithms with optimized transmission conditions. Its solution characterizes in each class of transmission conditions the one with the best performance of the associated waveform relaxation algorithm. We present the particular class of first order transmission conditions in detail...

In image processing, the Rudin-Osher-Fatemi (ROF) model [L. Rudin, S. Osher, and E. Fatemi, Physica D, 60(1992), pp. 259–268] based on total variation (TV) minimization has proven to be very useful. A lot of efforts have been devoted to obtain fast numerical schemes and overcome the non-differentiability of the model. Methods considered to be particularly efficient for the ROF model include the...

The performance of six variants of the successive overrelaxation methods (SOR) are considered for an algebraic system arising from a finite difference treatment of an elliptic equation of Partial Differential Equations (PDEs) on a triangular region. The consistency of the finite difference representation of the system is achieved. In the finite difference method one obtains an algebraic system ...

A Poisson-type equation arising in a commonly used numerical weather forecasting model is solved using an alternating direction implicit (ADI) method with Wachpress optimum parameters on a trapezoidal domain which coincides with the operational forecast domain. Various optimum parameter sequences were obtained for the corresponding squares which enclose the region under consideration, computati...

Interpreting the celebrated Rudin-Osher-Fatemi (ROF) model in a Bayesian framework has led to interesting new variants for Total Variation image denoising in the last decade. The Posterior Mean variant avoids the so-called staircasing artifact of the ROF model but is computationally very expensive. Another recent variant, called TV-ICE (for Iterated Conditional Expectation), delivers very simil...

In this work we analyze and compare two recent variational models for image denoising and improve their reconstructions by applying a Bregman iteration strategy. One of the standard techniques in image denoising, the ROF-model (cf. Rudin et al. in Physica D 60:259–268, 1992), is well known for recovering sharp edges of a signal or image, but also for producing staircase-like artifacts. In order...

We present a matrix language compiler CMC which translates annotated MATLAB scripts into Fortran 90 programs. Distinguishing features of CMC include its applicability to programs with sparse matrix computations and its capability of source-level optimization in MATLAB language. Different from other existing similar translators, CMC has an ability to generate codes based on information on the sh...

We propose a non-linear State Space representation to model ATM implied volatilities and to estimate the unobserved stochastic volatility for the underlying asset. We are able to estimate the average volatility risk premia and we can also address the presence of long memory in the unobserved volatility factor. We then applied our methodology to implied volatilities on currency options. These da...